Finding the difference in Helmholtz free energy using thermodynamic integration

[VVS2000]

TL;DR Summary

Finding out difference in helmholtz free energy using thermodynamic integration by using a ideal gas system as reference and lennard jones system as our system of interest

If there any solved papers or even python simulations to find this please share
I understood the process of thermodynamic integration but computationally I want to see how this integration of average of derivative of coupled potential energy is done

 

[Chestermiller]

You want to compare the result for a real gas with that for an ideal gas, right? Any particular scenario you want to look at?

 

[VVS2000]

You want to compare the result for a real gas with that for an ideal gas, right? Any particular scenario you want to look at?

Yeah for a lennard jones fluid, and basically I want to perform a computation of this integration process
But I am not able to understand how this integration is performed

 

[Chestermiller]

Yeah for a lennard jones fluid, and basically I want to perform a computation of this integration process
But I am not able to understand how this integration is performed

Please provide a specific example of a physical system passing from an initial state to final state.